Nonlinear Models Based on Quantiles in the Fitting of Growth Curves of Pepper Genotypes

Abstract

This study aimed to fit nonlinear regression models to model the growth of the characters fruit length (FL) and fruit width (FW) of pepper genotypes (Capsicum annuum L.) over time using the method of ordinary least squares (OLS); and identify the model with the best fit and compare it to the model obtained via nonlinear quantile regression (QR) in the 0.25, 0.5, and 0.75 quantiles. Three regression models (Logistic, Gompertz, and von Bertalanffy) and four fit quality evaluators were adopted: Akaike information criterion, residual mean absolute deviation, and parametric and intrinsic curvature measurements. Five commercial genotypes of pepper were evaluated. Characters FL and FW were evaluated weekly from seven days after flowering, totaling ten measurements. In the estimation by OLS, the Logistic and von Bertalanffy models were considered adequate according to the quality evaluators. In the comparison between the models above by OLS and QR, the superiority of models obtained by QR was verified for the character FL. For the character FW, QR was efficient in three out of the five genotypes, being a valuable alternative in the study of fruit growth.

Nonlinear Mixed-Effect Models to Describe Growth Curves of Pepper Fruits in Eight Cultivars Including Group Effects

“…This also shows that the fourth parameter of the Richards model, described earlier, did not make much difference in adjusting the fruit width since there were no gains compared to the Logistic model. Oliveira et al [6], also working with pepper width, observed that the Logistic model presented better AIC values for three of the five genotypes used when evaluating the fruits' width, corroborating this work's results. Other similar works studying fruit growth also concluded that the Logistic model stood out from the other studies [8,36,37].…”

“…The proximity of zero estimated by the MSE was also found by other authors [6], who used Quantile Regression and Ordinary Least Squares (OLS) for parameter estimation. The authors used an adjustment per individual considering fixed effects and included in the sample genotypes like those of pepper (first group) found in this work.…”

“…This can also be confirmed by looking at the estimates for the time to the tipping point for pepper ( β2 ) and pepper ( β5 ) in Table 5. Still about the length characteristic, the efficiency of the Logistic model was corroborated by Oliveira et al [6], who observed that for three of the five pepper genotypes, the Logistic model was the best fit. In the comparison made by this work, however, the Richards model was not included.…”

“…According to Rêgo et al [5], fruit weight, length, and diameter are essential in many horticultural crops, including pepper plants. In this context, evaluating the behavior of these characteristics throughout the crop cycle is fundamental for the researcher when deciding to develop appropriate management techniques and harvest fruits at appropriate growth stages [6].…”

“…This fact makes the method of nonlinear models an excellent alternative to adjust such growth behaviors. For pepper data, we can cite some research examples that used NLM to fit growth curves, such as [6][7][8].…”